nanomaterials
Article
Adsorption and Diffusion of Hydrogen in
Carbon Honeycomb
Qin Qin 1 , Tingwei Sun 1 , Hanxiao Wang 2 , Pascal Brault 3 , Haojie An 1 , Lu Xie 1, *
Qing Peng 4, *
1
2
3
4
*
and
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083,
China; qinqin@me.ustb.edu.cn (Q.Q.); s20180483@xs.ustb.edu.cn (T.S.); anhaojie@xs.ustb.edu.cn (H.A.)
Reactor Engineering and Safety Research Center, China Nuclear Power Technology Research Institute Co.,
Ltd., Shenzhen 518031, China; wanghanxiao@cgnpc.com.cn
GREMI UMR7344 CNRS, Université d’Orléans, BP6744, 45067 Orleans CEDEX 2,
France; pascal.brault@univ-orleans.fr
Physics Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Correspondence: xielu@ustb.edu.cn (L.X.); qing.peng@kfupm.edu.sa (Q.P.)
Received: 4 January 2020; Accepted: 12 February 2020; Published: 18 February 2020
Abstract: Carbon honeycomb has a nanoporous structure with good mechanical properties including
strength. Here we investigate the adsorption and diffusion of hydrogen in carbon honeycomb via
grand canonical Monte Carlo simulations and molecular dynamics simulations including strength.
Based on the adsorption simulations, molecular dynamics simulations are employed to study the
effect of pressure and temperature for the adsorption and diffusion of hydrogen. To study the effect
of pressure, we select the 0.1, 1, 5, 10, 15, and 20 bars. Meanwhile, we have studied the hydrogen
storage capacities of the carbon honeycomb at 77 K, 153 K, 193 K, 253 K and 298 K. A high hydrogen
adsorption of 4.36 wt.% is achieved at 77 K and 20 bars. The excellent mechanical properties of carbon
honeycomb and its unique three-dimensional honeycomb microporous structure provide a strong
guarantee for its application in practical engineering fields.
Keywords: hydrogen adsorption; carbon honeycomb; molecular dynamics; grand canonical Monte
Carlo simulations; pressure; temperature
1. Introduction
Hydrogen is a renewable energy source that can be used to replace fossil fuels with promising
application prospects. The key to utilize this clean energy source is the efficient storage of
hydrogen [1]. An effective way to improve hydrogen storage is to increase external pressure.
However, the hydrogen storage capacity rises quite slowly when external pressure reaches a certain
value. The introduction of porous materials could be a way to solve these problems, which adsorb
hydrogen with relatively low pressure [2]. Many research works show that porous materials including
zeolites [3], carbon-based nanomaterials (CBNs), and metal organic frameworks (MOFs) [4] have
certain hydrogen storage potential [5]. The design of porous materials with low density and high
porosity plays an important role in hydrogen storage.
Adsorption storage in porous materials is a new way to store hydrogen, which is considered to be
safe and reliable, and has high hydrogen storage efficiency [6]. Meanwhile, physisorption of hydrogen
on the porous material surface requires relatively small external pressure, low cost and simple material
structural design [2]. Nanoporous materials are considered to have the greatest potential in adsorption
storage due to the high adsorption surface area. Ma et al. [7] prepared a porous structure and found
that the porous structure has excellent adsorption characteristics. Among those known nanoporous
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materials, CBNs have lower density than both zeolites and MOFs [8]. It is reported that such materials
uptake and release more easily [9]. In addition, CBNs show tunable porosity and surface area since
there are many structural forms including graphene, fullerene, carbon nanotubes and their various
combinations [10,11]. Therefore, it is worth exploring the potential of new kinds of CBNs in hydrogen
adsorption storage.
There are lots of studies about the hydrogen adsorption inside porous carbon nanomaterials.
Active carbon is known as a kind of carbon material with high specific surface area. The reported
amount of adsorbed hydrogen is up to about 5 wt.% at 77 K, while it is about one order of magnitude
lower at room temperature under the same pressure [12,13]. Wu et al. [14] reported that the amount
of hydrogen physisorption in four-layer graphene sheets with interlayer spacing of 1.4 nm can reach
10 wt.%. Carbon nanotubes (CNTs) are also reported to have high hydrogen adsorption capacity [15,16].
Research shows that hydrogen adsorption on one side of graphene sheet can be up to 3 wt.% [17],
and pillared graphene reported by Wu et al. can reach a hydrogen adsorption of 4 wt.% [11].
Although some of those various combinations of CNT, graphene and fullerene exhibit outstanding
hydrogen storage capacity, synthesis is still challenging [18]. Recently the introduction of a template
carbonization process provides a new method for the synthesis of carbon nanoporous materials,
in which the template is carbonized and then removed to obtain a variety of carbon porous materials [19].
Khanin et al. [20] synthesised a carbon replica of zeolite experimentally. Thomas et al. [21] obtained
some carbon nanoporous structures by carbonization of faujasite zeolite template, and investigated
the adsorption capacity of these structures. In addition, a theoretical method has been performed to
simulate and predict carbon replica of template. Joshua et al. [22] investigated the adsorption and
diffusion of gas in a carbon replica of zeolite faujasite using the Grand Canonical Monte Carlo (GCMC)
method. Efrem et al. [19] investigated the synthesis of zeolite-templated carbon (ZTC) using chemical
vapour deposition technology and introduced a theoretical method to obtain the atomic structure of
ZTC from any template. This makes it possible to successfully predict a carbon replica of any specific
template, and gives carbon materials a more fascinating prospect in hydrogen storage.
Similar to ZTC, carbon honeycomb (CHC) has a nanoporous structure. Our previous study
illustrates that CHC possesses outstanding mechanical properties [23], which could form a strong
framework for hydrogen storage. It is natural to question to what extent the CHC can store hydrogen,
which motivated us to carry out this investigation.
This study aims to explore the capability of the hydrogen storage in CHC to extend the horizon of
the applications of CHC in hydrogen energy. It can be concluded from the literature [24] that during
the adsorption process, quantum confinement induces disorder on the positional, orientational, and
intramolecular structures of the adsorbed atoms. Therefore, the position, orientation and structure of
hydrogen atoms are not our focus. The ability of CHC to store hydrogen is quantified by changes in
the number of hydrogen atoms. The pressure and temperature effects on the hydrogen storage are
examined while the carbon framework of CHC was kept fixed. GCMC simulations are employed
to investigate the hydrogen storage capacity of CHC which has been experimentally synthesized
recently [23,25,26]. Based on the model after hydrogen adsorption, molecular dynamics (MD) methods
are utilized to investigate the diffusion of hydrogen confined in the carbon honeycomb. The effect of
pressure and temperature are investigated. To study the effect of pressure, we select the 0.1, 1, 5, 10, 15
and 20 bars. In addition, we study the hydrogen storage capacities of the carbon honeycomb at 77 K,
153 K, 193 K, 253 K and 298 K.
2. Methodology
The atomic structures of CHC and the percentage of carbon atoms’ hybrid method are presented in
Figure 1. CHC has a high structural stability due to its sp2 –sp3 hybridization and the sp2 and sp3 carbon
atoms result in porous structures [27]. The hybridization at the junction atoms of CHC are sp3 , and the
remaining atoms are sp2 . Graphene, a two-dimensional carbon structure, is a typical structure with
sp2 hybridization of carbon atoms. It exhibits outstanding physical, chemical, mechanical properties,
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thermodynamic and other properties [28,29]. Diamond is a typical structure with sp3 hybridization of
carbon atoms. Diamond is the hardest mineral in nature. It is widely used in precision grinding and
other industries.
Figure 1. (a) The schematic diagraph of carbon honeycomb (CHC) atomic structures. (b) The percentage
of hybrid method of carbon atoms. (c) The schematic diagraph of graphene. (d) The schematic diagraph
of diamond. The hybridization of CHC at the junction atoms are sp3 , and the remaining atoms are sp2 .
Graphene is a typical structure with sp2 hybridization of carbon atoms. Diamond is a typical structure
with sp3 hybridization of carbon atoms.
The density of CHC is 1.31 g/cm3 . Hydrogen adsorption is related to the porosity of porous
materials. Here, the Zeo++ package, an open source software, is employed to investigated the void
space representations of carbon materials [30]. For each calculation, the number of Monte Carlo samples
per atom is set to 100,000. The pore size distribution (PSD) is calculated with a small spherical probe of
0.5 Å radius so that more details can be detected. The pore size of CHC is 8.3 Å. It was
reported that
carbon materials with pore sizes between 7 and 12TÅ have the mostPpromising potential for hydrogen
storage, because the transport efficiency is low when the pore is too small and the adsorption amount
at room temperature is low when the pore is too large [17]. Therefore, the material used in this work is
suitable for hydrogen adsorption. When calculating
the accessible surface area (ASA) and accessible
volume (AV) fraction, the spherical probe with radius of 1.625 Å is utilized [31,32]. The accessible
surface area (ASA) and accessible volume (AV) fraction of CHC are 1071 m2 /g and 12.32%, respectively.
Before the GCMC
simulation, the CHC was relaxed by using isothermal-isobaric (NPT) ensemble
to reach equilibrium via MD simulations. The external pressure was zero at the relax stage.
The temperature in the relax stage was the same as that in the GCMC simulated, which are 77 K, 153
K, 193 K, 253 K and 298 K, respectively. The MD timestep was 1 fs and duration was 20 ps. Periodic
boundary conditions along x, y and z direction were used.
After equilibrating the system at the corresponding temperature, the GCMC simulations were
carried out to simulate hydrogen adsorption isotherms
at 77 K, 153 K, 193 K, 253 K and 298 K by
using the Large-scale Atomic Molecular Massively Parallel Simulator (LAMMPS) package (lammps-7
August 2019, Sandia National Laboratories, Albuquerque, USA) [33,34]. The Open Visualization Tool
(OVITO) [35,36] package (3.0.0-dev646, the OVITO software, Darmstadt, GER) was used for structure
and data analysis. In GCMC simulations the adsorption isotherms of hydrogen are calculated by
balancing the chemical potential µ with an imaginary ideal gas zone at specific temperature T and
pressure P, which is defined as [37]:
φPΛ3
(1)
µ = kB T ln
kB T
where kB and Λ represent Boltzmann’s constant and thermal de Broglie wavelength, respectively. φ is
the fugacity coefficient. adaptive intermolecular reactive empirical bond order (AIREBO) potential [38]
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is utilized to describe the interactions of carbon–carbon, carbon–hydrogen and hydrogen–hydrogen.
This potential ensures that hydrogen exists in molecular form, which is in line with reality. The carbon
structures are considered to be rigid in GCMC simulations. That is reasonable due to the high
stiffness of those carbon structures and it has been used in many previous studies to improve the
computational efficiency [10,11,39]. The number of grand canonical Monte Carlo (GCMC) steps
for hydrogen adsorption is 200,000 in GCMC simulation. The boundary of the simulation boxes is
considered as periodic and a time step of 0.1 fs is utilized. The timestep size is set for subsequent
molecular dynamics simulations. The timestep units is associated with each choice of units that
LAMMPS supports.
3. Results and Discussion
3.1. Mechanical Properties of Carbon Honeycomb
Materials used for hydrogen storage should not only have a high adsorption capacity, but also
sufficient mechanical strength. In our previous research, it can be concluded that CHC has fascinating
mechanical properties and potential application prospects [25,26]. We studied the mechanical properties
of CHC when stretching along the different tilt angle in the zigzag–armchair (x–y) plane. It can be
concluded that the mechanical properties of CHC in the x–y plane show anisotropy and the strength
of CHC decreases with the tilt angle increasing, which is similar to that of graphene. The effect of
temperature and vacancy-type defects on the mechanical properties of CHC were studied. The results
show that temperature affects the strength of CHC and the strength of CHC decreases as the temperature
increases. Vacancy defects affect the strength and fracture strain of the CHC. The strength is sensitive
to the location and bonding of the vacancies.
CHC has great application potential in many aspects for the outstanding mechanical properties,
which could be conducive to the storage of hydrogen. Hydrogen enters the internal pores of the CHC
and exerts a force on the structure.
3.2. Pressure Effect on the Hydrogen Adsorption
The effect of pressure on the amount of hydrogen molecules adsorbed inside CHC materials is
investigated at the temperature of 77 K. Figure 2 exhibits the variation of the mass fraction of adsorbed
hydrogen and the number of MC steps at pressures ranges from 0.1 to 20 bar. It can be seen from
Figure 2a that the hydrogen adsorption process in CHC could be divided into three stages: rapid
adsorption, slow adsorption and saturation. The adsorption of hydrogen molecules on the surface of
CHC occurs mainly at the relatively early stage of the GCMC simulations. The topography of different
pressures is shown in Figure 2b during the saturation phase (at the MC steps of 150,000).
At the pressure of 0.1 bar, the amount of adsorbed hydrogen molecules reaches saturation
rapidly, and this rapid adsorption stage lasts longer as the pressure rises. The chemical potential of
hydrogen in the simulation box is then close to the given value. Therefore, the adsorption rate of
hydrogen is gradually reduced until a stable saturation state is reached, indicating that the simulated
hydrogen reservoir is balanced with the imaginary ideal hydrogen zone at specified chemical potential.
The hydrogen adsorption processes from GCMC simulations are similar with previous report from
MD simulation [11].
The amount of adsorbed hydrogen increases as the pressure increases, as shown in Figure 2.
When the pressure is improved from 0.1 to 20 bar it increases 12-fold for CHC. The hydrogen adsorption
is about 4.36 wt.% for CHC at the pressure of 20 bar. The hydrogen adsorption is about 0.3 wt.%
for a single-walled carbon nanotube (SWNT) and 1.2 wt.% for SWNT after sonication in dimethyl
formamide [40] at 80 K and 10 bar hydrogen pressure. It is 2.2 wt.% and 3.6 wt.% reported by
Farida et al. for CNTs arranged in square and hexagonal lattices at 77 K and 10 bar [41]. The highest
hydrogen adsorption for graphene oxide framework materials is around 1.2 wt.% at 77 K [42,43].
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Figure 2. (a) The relationship between the mass fraction of adsorbed hydrogen and grand canonical
Monte Carlo (GCMC) steps (b) the topography of 150,000 MC steps under different pressures at the
temperature of 77 K for CHC.
3.3. Temperature Effect on the Hydrogen Adsorption
To investigate the hydrogen adsorption isotherms of CHC, the simulation system was kept at
a pressure range from 1 to 20 bar. Besides, temperature is another influencing factor affecting the
hydrogen storage capacity of porous materials. Different temperature conditions (77 K, 153 K, 193 K,
253 K and 298 K) are utilized to analyze the effect of temperature on the hydrogen adsorption in the
carbon structures.
The hydrogen adsorption isotherms for CHC at 77 K, 153 K, 193 K, 253 K and 298 K are presented in
Figure 3a. The isotherms are observed from Figure 3a, which corresponds to a previous report [10] since
the carbon materials are microporous (pore size is less than 2 nm) structures. At the low-pressure region
(<5 bar), the amount of hydrogen adsorption increases rapidly with increasing pressure, while the
amount of adsorption tends to increase slowly at the high-pressure region (>10 bar). The maximum
adsorption of hydrogen for CHC is about 4.36 wt.% at the temperature of 77 K and pressure of 20 bar.
Langmi et al. [44] reported that the hydrogen adsorption in ion-exchanged zeolites is 2.19 wt.% for
CaX, 1.96 wt.% for KX at 77 K and 15 bar. In addition, lots of research works show that the gravimetric
storage capacity of zeolites is generally below 3 wt.% [2,3,45–47]. The result shows that CHC are more
suitable for hydrogen storage than zeolites.
Figure 3a demonstrates that the hydrogen adsorption capacity of the CHC decreases as the
temperature increases from 77 K to 298 K. The kinetic energy of hydrogen molecules increases with
increasing temperature, so that more adsorption potential is required to adsorb hydrogen molecules
with higher kinetic energy. Therefore, the increase in temperature is not conducive to the adsorption of
hydrogen on the carbon nanoporous materials. Besides, at the same temperature the result shows that
the hydrogen storage capacity increases.
Based on the equilibrated models obtained from the GCMC calculations, MD simulations are
carried out to investigate the diffusion of hydrogen inside CHC. Five pressure points (1, 5, 10, 15 and
20 bar) are selected along the adsorption isotherms of hydrogen at 77 K, 153 K, 193 K, 253 K and 298 K,
respectively. MD simulations are performed for 100 ps in the NVT ensemble with a time step of 0.1 fs.
The mean squared displacements (MSD) are calculated from the trajectories to study the diffusion of
hydrogen atoms confined in the CHC. Supplementary Figure S1a–e shows the MSD-time curves in the
logarithmic coordinates. On the log-log scale, the linear correlation between MSD and time is detected.
The slopes of all the curves are around 1, showing an eventual diffusive behavior.
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Figure 3. (a) The hydrogen adsorption isotherms and (b) the diffusion coefficients for hydrogen
for CHC under different hydrogen pressure at the temperature of 77 K, 153 K, 193 K, 253 K and
298 K, respectively.
Figure 3b presents the variation of diffusion coefficients D of hydrogen adsorbed in CHC with
pressure at 77 K, 153 K, 193 K, 253 K and 298 K. The resulting diffusion coefficients are in the range of 2.4
to 25.1 10−4 *cm2 /s, which is of the same order of magnitude as hydrogen diffusion in zeolites reported
by Bar et al. experimentally [48]. At low pressure, the diffusion coefficient of hydrogen decreases
rapidly with the increasing pressure, while the rate of decrease in the diffusion coefficient slows down
at high pressure. Referring to Figure 3a,b, it can be seen that the variation of diffusion coefficients is
related to the adsorption amount of hydrogen. The increases in pressure leads to an increase in the
amount of adsorbed hydrogen, while the diffusion coefficient is reduced. At low pressure, as pressure
increases the amount of adsorbed hydrogen increases dramatically, so the diffusion coefficient of
hydrogen decreases rapidly. At the high-pressure zone, the diffusion coefficient drops slowly since
hydrogen adsorption is close to saturation.
It can be seen from Figure 3b that the diffusion coefficient of adsorbed hydrogen at 298 K is higher
than that at 77 K. At a low pressure of 1 bar, the diffusion coefficient for CHC increases by 3.2 times as
temperature increases from 77 K to 298 K. The increase in temperature improves the intensity of the
thermal motion of hydrogen molecules confined in microporous carbon, indicating that the diffusion
of hydrogen molecules is a thermal activation process. Therefore, the diffusion coefficient increases as
temperature increases.
4. Conclusions
In this study, the hydrogen adsorption capacity of the nanoporous materials of CHC is investigated
by using grand canonical Monte Carlo simulations and molecular dynamics simulations. The result
shows that low temperature and high pressure are conducive to hydrogen storage. At 77 K and 20 bars,
the maximum amounts of adsorbed hydrogen (4.36 wt.% for CHC) are observed. In addition, based on
the configuration obtained from GCMC simulations, the diffusion of hydrogen confined in the CHC
is studied via MD simulations. Results show that the diffusion of hydrogen is both pressure- and
temperature-dependent. The diffusion coefficient increases with a reduction in pressure since there is
less hydrogen at low pressure. A high diffusion coefficient is computed at high temperature showing
that hydrogen diffusion is a thermal activation process. In conclusion, as a newly nanoporous carbon,
CHC with high stiffness could be a promising material for hydrogen storage.
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It is worth noting that the classical MD simulations implemented in this study are unable to
account for the quantum effect that might play roles at low temperatures close to zero. Keep in
mind that hydrogen atoms follow one-dimensional motion along the nanopores of CHC. The average
thermal de Broglie wavelength of such one-dimensional motion of hydrogen is 1.99, 1.41, 1.26, 1.1,
and 1.0 Å at 77, 153, 193, 253, and 298 K, respectively, which is much less than the pore size of 8.3 Å.
Therefore, the influence of the quantum effect will not be significant. In spite of the limitation of the
method that ignores the quantum effect, our MD simulations have qualitatively captured the salient
features of hydrogen behaviors in the nanopores of CHC.
Supplementary Materials: The following are available online at http://www.mdpi.com/2079-4991/10/2/344/s1:
Figure S1: Mean squared displacements for hydrogen confined in CHC under different pressures and temperature,
Figure S2: Engineering stress-strain curves of carbon honeycomb for tensile loading, Video S1: the adsorption
process of hydrogen at the pressure of 10 bar and the temperature of 77 K for CHC, Video S2: the stretching
process along the z direction at the temperature of 77 K for CHC.
Author Contributions: Conceptualization, L.X. and Q.P.; methodology, Q.Q. and T.S.; formal analysis, L.X.;
investigation, T.S. and H.W.; writing—original draft preparation, T.S. and H.A.; writing—review and editing, L.X.,
Q.P. and P.B.; visualization, H.T.; supervision, Q.P. and Q.Q.; funding acquisition, L.X. All authors have read and
agreed to the published version of the manuscript.
Funding: The authors would like to thank the financial support to this study from Joint Research
Program of Ministry of Education (6141A02022242) Fundamental Research Funds for the Central Universities
(FRF-TP-19-014A2).
Conflicts of Interest: No potential conflict of interest was reported by the authors.
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